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Wow that is cool and though I totally agree with the methods you have and the 
attendant good results I notice that in the course of the discussions AM PM 
equal altitude shots are not discussed or I am missing something. As I am 
sure you are no doubt well aware of after meridian passage you set your 
sextant to a number of AM altitudes, wait for the Sun's tangency, mark the 
times, average each pair for LAN, inspect each pair for consistancy, and 
either average them or take one pair and solve for longitude. Thanks much and 
keep on "shootin' and computin'"!
Mike Burkes
>
>
> Latitude and Longitude by Sunline near LAN.
>
> This seems to be one of Frank�s pet sights and is outlined in the
> more recent editions of Bowditch (1995 and newer). Essentially we are
> taking a range of altitudes over a period of time before, during, and
> after the sun crosses the meridian of the observer (LAN). The raw
> sextant sights are then plotted on the Y-axis, and time (GMT) is
> plotted on the x-axis. Once plotted, the curve should be a parabola
> and can be folded so that the two halves mirror each other. Depending
> on the number of sights and accuracy of those sights, the curve should
> be fairly uniform. The crease, when crossing the x-axis should show
> you the exact time of LAN. This time can be then entered into the
> almanac to find the exact GHA of the sun at that moment. GHA
> converted to Longitude should give the Longitude of the observer at
> the moment of LAN. This curve will be skewed to a greater or larger
> extent based on the change in declination of the body and the North/
> South component of the ship�s motion. Because of these factors, if
> you use raw data, a prudent navigator would put only as much faith
> into the position as can be reckoned knowing that errors may exist due
> to these factors.
> To obtain Latitude, the nearest sight to the time of LAN (which
> should be the maximum altitude, or very close) must be converted to Ho
> then the z-distance and declination applied as a straight LAN problem.
> A second method to obtain Latitude and Longitude from these numbers
> is to reduce the data as standard sunlines. A great number of sun
> lines reduced and plotted should give an accurate position if done
> correctly. This is best done with a computer reduction and plotter as
> the sheer number of sights to reduce to obtain good accuracy will be a
> burden to attempt using tables or even calculators.
> This method can contain several errors and can cause some
> difficulties. I think that the best time and place for this sort of
> sight is near the solstice (when the change in declination is quite
> small) and in the tropics (where the change in altitude is fairly
> rapid over time.) Fast moving ships, especially with Northerly or
> Southerly courses, will also cause a skewing of the curve as the
> altitude will change with the change in Latitude.
> I performed this sight in late May in Latitude 15 deg North, while the
> ship was drifting due to engine problems (crs 270, Spd 0.6 knots).
> This allowed for a change in Altitude of about 35� of arc over a
> period of 24 minutes. During this time, I shot 31 sunlines and
> graphed them. One sight proved to be in error as it skewed the curve,
> but not so much as to cause a problem. The change of declination from
> start to finish was 0.2� so the effects of time were minimal in this
> case. Near an equinox this error would have been much greater and
> probably would have skewed the curve visibly.
> With the graph and a bit of eyeball interpolation, I was able to
> determine the time of LAN within 2 seconds with a corresponding error
> of Longitude of about 0.7� which is certainly an excellent result. I
> saw the first change in altitude of the sun 3 seconds after the time
> of LAN computed from the GPS longitude, and used this for my latitude
> line, providing a 0.2� error south is Latitude. This gave a total
> position error of 0.9 nm which is quite good for Celnav at sea.
> After the graphic reduction, I plugged 25 of the sights (the maximum
> allowed) into the computer and did a standard running fix via
> Celestial LOP�s (lots of sunlines). I excluded the obviously flawed
> sight and several of the 30-second interval sights near LAN, keeping
> all of the other sights some distance from LAN. The error in Latitude
> from this method was 0.1� and the error in Longitude was 0.4� This
> gave me an error in position of 0.4 nm at the time of LAN. This
> method under these circumstances provided a very good position.
> The attached spreadsheet (MS Excel) shows the raw data. The first
> column shows the number of the sight. All shots were shot after 12
> PM, and the second column shows the minutes of the noon hour, while
> the third column shows seconds. The fourth column �time� is decimal
> minutes. Next is the Hs measure, first in degrees, followed by
> minutes of arc to the nearest tenth. Next we have Hs in decimal
> minutes. The last two columns were time and Hs which were used for
> the plot which is below and should be printable as a separate page for
> people to try at a decent scale. The box on the right is the data in
> a more concise form including errors as computed by sailings. I also
> included a short form of my Lat by LAN computation.
>
> The conclusion I find with this method is that if it is done at a time
> and place to eliminate most of the variables, it can be utilized at
> sea without too many calculations to determine both latitude and
> longitude. The real trouble begins if your latitude varies greatly
> from your declinations, you are moving rapidly north to south, or you
> don�t have the hour it takes to shoot and reduce this sight. I still
> believe that an AM sunline crossed with a LAN is your most convenient
> method to get a noon fix and can be used without thinking of all of
> the variables that will creep in using this method in various
> locations and at times more distant to the Solstice.
>
> I am attaching the MS Excel spreadsheet to my next post that I used
> for the graphic display. Unfortunately I cannot electronically
> reproduce the sunline method of reduction, but it uses the same data
> as on the spreadsheet.
>
> Jeremy
> >

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